820 research outputs found
Conservative constraint satisfaction re-revisited
Conservative constraint satisfaction problems (CSPs) constitute an important
particular case of the general CSP, in which the allowed values of each
variable can be restricted in an arbitrary way. Problems of this type are well
studied for graph homomorphisms. A dichotomy theorem characterizing
conservative CSPs solvable in polynomial time and proving that the remaining
ones are NP-complete was proved by Bulatov in 2003. Its proof, however, is
quite long and technical. A shorter proof of this result based on the absorbing
subuniverses technique was suggested by Barto in 2011. In this paper we give a
short elementary prove of the dichotomy theorem for the conservative CSP
Anomalous tunneling of bound pairs in crystal lattices
A novel method of solving scattering problems for bound pairs on a lattice is
developed. Two different break ups of the hamiltonian are employed to calculate
the full Green operator and the wave function of the scattered pair. The
calculation converges exponentially in the number of basis states used to
represent the non-translation invariant part of the Green operator. The method
is general and applicable to a variety of scattering and tunneling problems. As
the first application, the problem of pair tunneling through a weak link on a
one-dimensional lattice is solved. It is found that at momenta close to \pi the
pair tunnels much easier than one particle, with the transmission coefficient
approaching unity. This anomalously high transmission is a consequence of the
existence of a two-body resonant state localized at the weak link.Comment: REVTeX, 5 pages, 4 eps figure
Galois correspondence for counting quantifiers
We introduce a new type of closure operator on the set of relations,
max-implementation, and its weaker analog max-quantification. Then we show that
approximation preserving reductions between counting constraint satisfaction
problems (#CSPs) are preserved by these two types of closure operators.
Together with some previous results this means that the approximation
complexity of counting CSPs is determined by partial clones of relations that
additionally closed under these new types of closure operators. Galois
correspondence of various kind have proved to be quite helpful in the study of
the complexity of the CSP. While we were unable to identify a Galois
correspondence for partial clones closed under max-implementation and
max-quantification, we obtain such results for slightly different type of
closure operators, k-existential quantification. This type of quantifiers are
known as counting quantifiers in model theory, and often used to enhance first
order logic languages. We characterize partial clones of relations closed under
k-existential quantification as sets of relations invariant under a set of
partial functions that satisfy the condition of k-subset surjectivity. Finally,
we give a description of Boolean max-co-clones, that is, sets of relations on
{0,1} closed under max-implementations.Comment: 28 pages, 2 figure
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